Nomographic device



3 Sheets-Sheet 1 Filed Aug. 5, 1954 I I I I I 2 Z 1 1 I INVENTOR JOHN GARRETT HOLT ATTORNEY Dec. 27, 1955 J. G. HOLT 2,728,525

NOMOGRAPHIC DEVICE Filed Aug. 5, 1954 3 Sheets-Sheet 2 INVENTOR JOHN GARRETT HOLT ATTORNEY Dec. 27, 1955 J, HOLT 2,728,525

NOMOGRAPHIC DEVICE 5 Sheets-Sheet 3 Filed Aug. 5, 1954 I I II 3.25 4. C I I Cl IC I I I h I I d I; I I f 90 Io Ll CI l L 4 A' l A I l l l I I I' 6 C C" AP & 'f' All INVENTOR JOHN GARRETT HOLT ATTORNEY United States Patent NOMOGRAPHIC DEVICE John Garrett Holt, Flushing, N. Y., assignor to Research Corporation, New York, N. Y., a corporation of New York Application August 5, 1954, Serial No. 447,998

6 Claims. (Cl. 235-61) This invention relates to a calculating device for facilitating the computation of radiation dosage produced by a radium source located within a patient.

In the course of interstitial or intravacitary treatment with linear radium sources, it is quite often desirable to know the actual dose rate at a number of selected points within the patient. Anyone who has ever attempted to insert radium sources according to a pre-arranged pattern, will readily attest that in practice the actual distribution of radium sources within the patient often varies considerably from the precalculated geometric arrangement. In order to control the total dose, it is, therefore, useful to know the actual dose rate at a number of critical points. Unfortunately, these points are usually inaccessible to direct dose rate measuring devices, and one is faced with the problem of calculating the particular dose rates. In practice, this has usually been a chore of from some four to six hours.

It is a primary object of the invention to provide a simple, inexpensive device which can readily be used by the technician of ordinary skill in this field, and which enables the dosage to be calculated, in many cases, in approximately ten percent of the time formerly required.

Another object is to provide a nomographic device for the purpose stated, which can be readily used with sources of different intensity or radiation rate.

The specific nature of the invention as well as other objects and advantages thereof will clearly appear from a description of a preferred embodiment as shown in the accompanying drawing, in which:

Fig. 1 is a schematic cross-sectional view of a patient showing the relation of the X-ray radiograph views to the subject;

Fig. 2 is a top view of the nomographic wheel of the invention;

Fig. 3 is an enlarged fragmentary sectional view taken on line 3-3 of Fig. 2, and

Fig. 4 is a geometric construction showing the principle of operation of the device.

The general technique for determining or measuring the dosage produced by one or more radioactive sources actually inserted in a patient requires that two mutually perpendicular radiographs or X-ray photographs be taken. The set-up for this is shown in Fig. 1. A cross section of the patient is shown at 2, with the inserted radium source at 4. Radiograph films 6 and 8 are arranged adjacent to the subject and at right angles to each other as shown. Film 6 is termed the anterior-posterior film and is more commonly referred to as the AP film. Film 8 is a lateral X-ray view of the subject and is accordingly referred to as a lateral film. Two X-ray sources 10 and 10 are shown for the two'radiographs, but it will be understood that in practice, the same source will usually be employed and will be rotated 90 between exposure, only one film being exposed at a time. Due to the divergence of the X-rays from the source, objects on the films are not shown in their true size, but are magnified. The magnification 2,728,525 Patented Dec. 27, 1955 for the AP view is not necessarily the same as the lateral magnification, because the height of the radium above the film is not necessarily the same in both cases, even if the X-ray source is at the same distance from the subject in both views. The actual magnification is, therefore, determined by placing a coin or ring 12 of known dimension on the exterior of the patient, in the plane that contains the radium, and in a position parallel to the film. The ring will, therefore, have the same magnification in the film as the average plane of the radium. The magnification factor is then readily found by dividing the diameter or other significant dimension of the ring on the film by the true diameter of the ring, and the magnification factor For example, as shown in Fig. 1, if the true diameter of the ring is indicated as D, then the magnified diameter will be D on the film and the magnification factor is the ratio of D to D.

It is now required to determine from the developed films the distance between the center of the radium source 4 and one or more control points, which are the points at which the dosage provided by this radium source is to be determined. it will be understood that this control point is in the general case not in a common plane with the radium source parallel to either of the two films. The control point is often an anatomical feature which can be readily discerned on the films. If the control point is not an anatomical feature, or if it is not determined by markers visible on the film, it is necessary to construct the hypothetical AP and lateral projections of the control point on both films with considerations of magnification, distortions, etc., as will be well understood by those skilled in the art. Each film will now show the projection of the radial distance between the radium point and the control point, and from these projections it is necessary to determine the true distance between the two points. This can, of course, be done by a series of rather tedious calculations, which are both time consuming and subject to arithmetic error so that considerable checking is required. In accordance with the invention, a simple nornographic slide rule is provided which will now be described, and which enables these calculations to be simply, rapidly and correctly completed in a few minutes.

Referring to Fig. 2, the slide rule is shown as comprised of two concentric superimposed discs of transparent material, suitably fastened together to permit relative rotation, for example, by a grommet 16. The uppermost disc 18 is preferably made smaller in diameter than the lower disc 20, which facilitates rotation and other movement of the two discs together as a unit, since this is required in the normal operation of the device. Sufficient friction is provided between the two discs so that, while they may be readily rotated relative to each other, they will also tend to remain in any set position without relative angular displacement. The grommet 16 is preferably made fairly fiat on the bottom as shown at 17 in Fig. 3, to facilitate placing the disc on the surface of a radiographic film.

The upper disc 18 has in one quadrant a ruled grid 22 with x and y coordinants as shown. The lower disc contains the reference crosslines 24 and 26, a protractor 23 and a dose rate scale 30, which reads radiation dose rates produced by a linear radium source (active length 1.5 cm.) in r/ mg.-hr. as a function of the radius of the wheel. The rotating grid, protractor and reference crosslines are used to solve for internal distances from the bi-planar radiographs, while the r/l00 mg.-hr. scale gives the dose rate for any particular distance. The manner in'which the wheel is used with the two radiographs previously taken will now be described.

On each film, the centers of all radium sources should be marked and the corresponding points suitably labeled, for example, Ri,2 i

On the lateral film a line (L1) should be drawn through the projection of the control point being computed, and parallel to the plane of the AP radiograph. On the grid of the wheel 18, the X-axis is assumed to correspond to the AP coordinate and the Y-axis to correspond to the lateral coordinate. The reference line is defined as the line from the center of the grommet 16 to the 0 mark on the protractor. The angle 6:; is now set corresponding to the AP magnification previously determined. This angle, as shown in Fig. 2 is set between the reference line 26 and the X-axis in such a way that the reference line falls within the grid 22, as shown in the figure. This angle is calculated from the magnification factor M as follows:

are cosine 1 0 Now with the origin of the grid on the desired control point, the wheel is tacked or pinned in position with a pin through the center of the grommet. The entire nomographic wheel is now rotated as a unit, without changing the angle setting, on the film until the reference line 26 passes through radium center R1, which always clearly shows in the film. Now the X-coordinate of R1 on the X-axis of the grid should be marked and suitably labeled, for example, X1. This is the projection in the plane of the AP film of the desired distance.

The nomographic wheel is now removed from the AP film and the angle 02' set corresponding to the lateral magnification, between the reference line and the Y-axis. As previously explained, this angle is usually not the same as for the AP film. The center of the wheel is now placed on line L1 and the wheel shifted along the line until the reference line 26 is perpendicular to L1 and also passes through radium center Rt. The Y coordinate of R1 is now marked on the Y-axis and labeled Y1. This is the projection of the desired distance on a plane at right angles to the first plane. Therefore, point Si (X1, Y1) that is defined by the intersection of coordinates X1 and Y1 is the true distance desired, since d /x +y Point Si is now rotated to scale 30 on the lower disc by rotating disc 18 on disc 20, and the contribution of radium source R1 to the control point may be read directly and immediately in r/ 100 1ng.-hrs. This should be multiplied by the number of milligrams in the radium source to read r/ hr.

This process should be repeated for all other radium sources and their contributions at the control point should be added to find the total dose rate. Similarly, if it is desired to determine the dosage at more than one control point, the above steps should be repeated for all other desired points.

In order to understand how the above steps produce the desired result, reference is made to Fig. 4. In this figure, location of the radium source 4 is indicated at point A,

and the desired control point at point C. The AP film plane is indicated at 6 and the lateral film plane at 8. The actual projection of point C on plane 8 from radium source 10 will be point CM. However, for the present purpose, since it is desired to find the actual distance between points C and A, it will be assumed in the following construction that there is no magnification. This is justified by the initial use of the magnification factor to reduce the magnified distances to the true distances.

The following geometric construction is assumed:

A. By parallel projection on the LAT plane project C and A into C and A respectively; on the AP plane project C and A into C" and A respectively.

B. Construct plane M through point A and parallel to plane AP.

C. Plane M1 cuts plane LAT in line L1.

D. Let line C-C cut plane M1 at C1; C1 projects into L on line Li.

E. Distance (CA) =(C A) +(C C) It will now be apparent that distances h and k correspond to distances Y and X in the procedure previously described, and that distance d corresponds to distance S1 on the quadrant.

The above procedure assumes that the isodoses around a linear radium source are spheres in space or circles in a plane. This is sufiiciently true provided that the distances from the point of interest to the center of the radium source is at least one-half the active length, and that small regions near the ends of the radium needle are excluded. For practical conditions, these assumptions are, of course, entirely reasonable. Results obtained under practical conditions indicate that the maximum error of the calculated distance in no case exceed the inherent error of the measurement, and that the device is therefore sufficiently accurate for all actual use.

It will be apparent that the embodiments shown are only exemplary and that various modifications can be made in construction and arrangement within the scope of my invention as defined in' appended claims.

I claim:

1. A radiation dosage calculator comprising two superimposed transparent scale sheets fastened together at a common origin point for relative rotation about said point, one of said sheets bearing a protractor scale drawn about said common origin point, and a radiation dosage scale on a radius extending from said point, the other of said scale sheets bearing a quadrant extending from said common origin point and a ruled grid in said quadrant said radiation dosage scale being correlated with the line spacing on said grid, and means at said common origin point enabling rotation of both scale sheets together as a unit about said point on a surface against which the unit is placed. 7

2. The invention according to claim 1, wherein said quadrant-bearing sheet is the upper sheet.

3. The invention according to claim 1, wherein both of said sheets comprise concentric circular discs.

4. The invention according to claim 3, wherein the diameter of the upper disc is substantially smaller than that of the lower disc.

5. The invention according to claim 1, wherein the upper surface of the top sheet is slightly roughened to retain pencil marks.

6. The invention according to claim 1, wherein said last means provides an aperture in said common origin point.

References Cited in the file of this patent UNITED STATES PATENTS 

1. A RADIATION DOSAGE CALCULATOR COMPRISING TWO SUPERIMPOSED TRANSPARENT SCALE SHEETS FASTENED TOGETHER AT A COMMON ORIGIN POINT FOR RELATIVE ROTATION ABOUT SAID POINT, ONE OF SAID SHEETS BEARING A PROTRACTOR SCALE DRAWN ABOUT SAID COMMON ORIGIN POINT, AND A RADIATION DOSAGE SCALE ON A RADIUS EXTENDING FROM SAID POINT, THE OTHER OF SAID SCALE SHEETS BEARING A QUADRANT EXTENDING FROM SAID COMMON ORIGIN POINT AND A RULED GRID IN SAID QUADRANT SAID RADIATION DOSAGE SCALE BEING CORRELATED WITH THE LINE SPACING ON SAID GRID, AND MEANS AT SAID COMMON ORIGIN POINT ENABLING ROTATION OF BOTH SCALE SHEETS TOGETHER AS A UNIT ABOUT SAID POINT ON A SURFACE AGAINST WHICH THE UNIT IS PLACED. 